Step-by-Step Age Calculation

To find the mother's age, we need to work through the statements, starting with the one known age (the sister's) to find the age of each person in sequence.

1. Find "My" Age
   • We are given that the sister is 12 years old.
   • The statement says, "I am... three years older to my sister."
   • My Age = Sister's Age + 3 = 12 + 3 = 15 years old.
2. Find the Brother's Age
   • The statement says, "I am five years younger to my brother."
   • This means the brother is 5 years older than me.
   • Brother's Age = My Age + 5 = 15 + 5 = 20 years old.
3. Find the Mother's Age
   • The statement says, "My mother is twice as old as my brother."
   • Mother's Age = 2 × Brother's Age = 2 × 20 = 40 years old.

Conclusion

The mother is 40 years old.